
theorem
  3407 is prime
proof
  now
    3407 = 2*1703 + 1; hence not 2 divides 3407 by NAT_4:9;
    3407 = 3*1135 + 2; hence not 3 divides 3407 by NAT_4:9;
    3407 = 5*681 + 2; hence not 5 divides 3407 by NAT_4:9;
    3407 = 7*486 + 5; hence not 7 divides 3407 by NAT_4:9;
    3407 = 11*309 + 8; hence not 11 divides 3407 by NAT_4:9;
    3407 = 13*262 + 1; hence not 13 divides 3407 by NAT_4:9;
    3407 = 17*200 + 7; hence not 17 divides 3407 by NAT_4:9;
    3407 = 19*179 + 6; hence not 19 divides 3407 by NAT_4:9;
    3407 = 23*148 + 3; hence not 23 divides 3407 by NAT_4:9;
    3407 = 29*117 + 14; hence not 29 divides 3407 by NAT_4:9;
    3407 = 31*109 + 28; hence not 31 divides 3407 by NAT_4:9;
    3407 = 37*92 + 3; hence not 37 divides 3407 by NAT_4:9;
    3407 = 41*83 + 4; hence not 41 divides 3407 by NAT_4:9;
    3407 = 43*79 + 10; hence not 43 divides 3407 by NAT_4:9;
    3407 = 47*72 + 23; hence not 47 divides 3407 by NAT_4:9;
    3407 = 53*64 + 15; hence not 53 divides 3407 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3407 & n is prime
  holds not n divides 3407 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
